For instance, libraries are funded by both federal and local sources. There is only one party that consistently wants to remove that funding (hint @which one: https://www.publishersweekly.com/pw/by-topic/industry-news/l...)

How much additionally is spent is locally determined, yes, and here you see that disparity as well. In Georgia, a heavily GOP state where I have family, the online catalog is pretty meager, even for major cities. While they have PINES for the less populous counties, a state-wide interlibrary loan program, it only is for physical books. Access to electronic resources is anemic. In California, a heavily Dem state where I live, the online resources tend to be excellent (especially if you're in larger counties/cities), not only having an extensive online catalog, but a lot of extras (Kanopy, Hoopla, language learning stuff, etc).

But even all that aside, the -effectiveness- is curtailed by federal effects. Online resource access, extremely relevant under COVID, requires stable internet access. But unfortunately, that's not always available. Attempts to treat internet as a utility, to financially fund broadband rollout nationwide, have failed, due to one particular party preferring it staying privatized and purely for profit. Programs to create financial incentives to offset the cost even where it is rolled out have been created, but only under one party, and the other seems inclined to defund or cancel them. Attempts to allow municipalities to roll out their own broadband to be able to offer faster speeds without data caps at lower prices have been fought tooth and nail, again, by one particular party, on behalf of preventing governmental 'competition' with the private sector.

Etc. In short, while you're right that localities are run by both major political parties, both the explicit statement you make that funding is local (only), and the implicit belief you're relying on that you can distance local effect from federal decisions, are wrong.